Definitions

Question 1

lattice

Answer 1

infinite set of points defined by integer sums of a set of linearly independent primitive lattice vectors = infinite discrete set of vectors where addition/subtraction of any 2 vectors in the set gives a 3rd vector in the set

Question 2

what are lattice points described as?

Answer 2

R = n1a1 + n2a2 + n3a3

Question 3

what’s an important property of lattices that defines them?

Answer 3

the environment of any given point in the lattice is equivalent to the environment of any other given point

Question 4

unit cell

Answer 4

region of space such that when many identical unit cells are stacked together, it completely fills all of space and reconstructs the full structure

Question 5

primitive unit cell

Answer 5

smallest possible unit cell = unit cell containing exactly 1 lattice point

Question 6

why do we sometimes choose a conventional unit cell?

Answer 6

easier to work with than a primitive unit cell

Question 7

Wigner-Seitz unit cell

Answer 7

for a given lattice point, it’s constructed by considering all points in space which are closer to that given lattice point than to any other lattice point

Question 8

basis

Answer 8

description of objects in the unit cell with respect to the reference lattice point in the unit cell

Question 9

reciprocal lattice condition

Answer 9

given a direct lattice of points R, a point G is a point in reciprocal lattice if e^(iG.R) = 1 for all points R of direct lattice

Question 10

property of primitive lattice vectors of the reciprocal lattice

Answer 10

ai.bj = 2πδij

Question 11

lattice plane

Answer 11

= crystal plane = plane containing at least 3 non-collinear points of a lattice

Question 12

family of lattice planes

Answer 12

infinite set of equally separated parallel lattice planes - taken together, they contain all points of the lattice

Question 13

spacing between lattice planes

Answer 13

d = 2π/Gmin. Gmin = min length reciprocal lattice vector in this normal direction

Question 14

Miller indices

Answer 14

notation for describing lattice planes (can be negative)

Question 15

first Brillouin zone

Answer 15

all k points which are closer to 0 than to any other reciprocal lattice point

Question 16

second Brillouin zone

Answer 16

all k points where point 0 is the second closest reciprocal lattice point to that point

Question 17

Brillouin zone

Answer 17

any primitive unit cell of the reciprocal latice

Question 18

structure factor

Answer 18

accounts for scattering power of basis atoms within conventional unit cell